Entropy method comprehensive evaluation analysis process
1. Case background
At present, there is a piece of data, which is the score of each brand car in each dimension. Now I want to use the entropy method to make a comprehensive evaluation and get the comprehensive score of each brand car, so as to compare the advantages and disadvantages of models and provide consumers with a basis for car purchase.
The data is as follows (the data is fictitious and has no practical significance):
2. Data processing
Using the entropy method for analysis requires data processing, including data direction processing and data dimension processing.
(1) Direction processing
When the data directions are inconsistent, direction processing is required to eliminate the influence of different data directions. According to different directions, data can be divided into positive indicators and negative indicators. Positive indicators refer to indicators with larger data, such as GDP; negative indicators refer to indicators with smaller data, such as Air Pollution Index. Direction processing is to positively process positive indicators and reversely process negative indicators, so that after processing, the data direction is completely consistent.
For the fuel consumption and cost of the vehicle in the case, consumers generally hope that the smaller the better, so these two indicators are negative indicators and need to be reversed; while the power, safety, maintainability and operability of the vehicle , generally hope that the bigger the better, these 4 indicators are positive indicators and need to be positively processed.
In SPSSAU, you can use the generate variable -> forward/reverse processing function, the operation is as follows:
The above figure shows the reverse processing operation of negative indicators, and the positive processing operation of positive indicators is the same as above.
(2) Dimensional processing
After eliminating the influence of data direction, it is also necessary to eliminate the influence caused by different data units, that is, perform dimensional processing. SPSSAU provides more than a dozen dimensional processing methods. Here, it is recommended to use data normalization for processing.
In this case, because the forward/reverse processing has been carried out in the above analysis, and the forward/reverse processing can solve the problem of direction and dimension at the same time, so there is no need to perform normalization processing again. After the data processing is completed, the entropy method analysis is carried out next.
3. Analysis of entropy method
The entropy method is one of the objective weighting methods, and the entropy value is a measure of uncertainty. The entropy method is used to determine the weight of indicators based on the degree of variation of the indicators at the numerical level. Due to the high dependence on objective data, the application of the entropy method avoids possible deviations caused by human factors to the weight results of indicators. The entropy value method uses information entropy to calculate the weight value of each index, which provides a basis for multi-index comprehensive evaluation.
Use the SPSSAU entropy method to analyze the processed data, check [Comprehensive Score] before analysis, and SPSSAU will automatically save the comprehensive score of each variable during analysis, and finally use it for comprehensive evaluation. You also need to check [Non-negative translation] before the analysis. The reason is that the calculation process of the entropy method contains logarithmic operations, and when the data has 0 or negative numbers, logarithmic operations cannot be performed, so SPSSAU provides non-negative translation functions. If The data is less than or equal to 0. At this time, the translation unit is: the absolute value of the minimum value + 0.01. It is guaranteed that all the data are positive numbers and can be calculated normally. SPSSAU operates as follows:
The entropy method calculates the weight results in the following table:
It can be seen from the above table that the weight values of power, safety, maintainability, operability, fuel consumption, and cost calculated by using the entropy method are 0.153, 0.118, 0.130, 0.257, 0.137, and 0.206, respectively.
Entropy method calculation formula:
(1) Information entropy value e
① Calculate the proportion of the i-th sample value under the j-th indicator
② Calculate the information entropy of each index (column)
Among them, k=1/ln(n);
(2) Information utility value d
(3) Weight coefficient value w
The obtained weight value will be used for subsequent comprehensive score calculation.
4. Comprehensive score
(1) Significance of comprehensive score
The comprehensive score is the decisive indicator for the final comprehensive evaluation of the entropy method. After obtaining the weight of each indicator, the data of each indicator is multiplied by the corresponding weight and then accumulated, which is the "comprehensive score". The comprehensive score can be used to measure the comprehensive level of each sample, and the higher the comprehensive score, the better the sample.
This indicator does not need to be calculated manually, because before the analysis, [Comprehensive Score] is checked, so SPSSAU will automatically complete the calculation and save it in [My Data].
(2) Comparison of pros and cons
The composite score data generated by SPSSAU is as follows:
Analysts download the data locally, sort the comprehensive scores, and compare the pros and cons of the samples. You can also use the Rank ranking function in the SPSSAU generated variable to rank the composite score. The operation is as follows:
Finally, after downloading the data, use Excel to sort out the comprehensive score ranking of each brand car as follows:
Judging from the analysis results, among the 7 brand cars involved in the analysis, the vehicle with the highest comprehensive score is vehicle 6, and the vehicle with the lowest comprehensive score is vehicle 5. It shows that vehicle 6 is the best in all aspects of the 7 vehicles, and vehicle 5 is the worst.
6. Summary
This analysis uses the entropy method to comprehensively evaluate 7 types of brand vehicles. Before the entropy method analysis, the data is firstly processed in direction and dimension to eliminate the influence of inconsistency in direction and unit. Then use SPSSAU to analyze the entropy value method to obtain the weight value of each index and the comprehensive score value of each sample. After ranking and comparing the comprehensive scores, it is obtained that the best vehicle in all aspects is vehicle 6, and the worst vehicle is 5. The analysis is completed.